Hi @Eagle76
In my case I use the MS Graph API to manage my teams and using Azure APP permissions as well.

There is still no MS Flow action to "manage" MS Team members, but something you can try is using the O365 groups action "add members to group". You could connect the Team with a O365 group - if isn't done yet (Taking into account that a MS Team has by default a O365 group on behind) and use it!
Can you test it and let me know? 🙂
Regards